Question: Problem: Suppose you have a recurrent chain in continuous time with transition rate Q(0,j)from state 0 to state j > 0. Starting in state 0,

Problem: Suppose you have a recurrent chain in continuous time with transition rate Q(0,j)from state 0 to state j > 0. Starting in state 0, let H(0,j) be the total time spent in state 0 before the first jump from 0 to j.

a) What is the distribution of H(0,j)?

b) What is the joint distribution of H(0,j) and H(0, k) for different j and k ?

In each case,explain as best you can.

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